Exercise 4¶

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You can start working on your copy of Exercise 4 by accepting the GitHub Classroom assignment.

Exercise 4 is due by the start of lecture in week 5.

You can also take a look at the open course copy of Exercise 4 in the course GitHub repository (does not require logging in). Note that you should not try to make changes to this copy of the exercise, but rather only to the copy available via GitHub Classroom.

Start your assignment

You can start working on your copy of Exercise 4.1 by accepting the GitHub Classroom assignment.

Exercise 4.1 is due by the start of lecture in week 5.

You can also take a look at the open course copy of Exercise 4.1 in the course GitHub repository (does not require logging in). Note that you should not try to make changes to this copy of the exercise, but rather only to the copy available via GitHub Classroom.

Hints for Exercise 4¶

P1: Calculating dh/dt (see also hint below)¶

For the calculate_dhdt function, you should ensure the value you return is negative. The stream-power itself can be positive, but returning a negative value ensures the stream-power equation acts to lower the topography.

\[\begin{equation} \Large \frac{dh}{dt} = -K A^{m} S^{n} \end{equation}\]

P1: Calculating the topography slope¶

In order to be able to calculate stream-power erosion from a river channel profile we first need to estimate both the upstream drainage area and calculate the topographic slope. You have hopefully already calculated the drainage area using your drainage_area function, and now we can turn our focus to the slope. Calculating the slope is not necessarily a difficult thing with NumPy, but you do need to be careful how you do it.

The first thing to recognize is that the slope at any given point will simply be the difference in elevation between that point and a neighboring point divided by the horizontal distance between them. In other words, slope is the change in elevation divided by the change in horizontal distance. You could calculate this by hand, but NumPy has some useful functions for this, including np.diff. Below, you can see how to use np.diff to calculate the channel slope.

slope = np.diff(topography)/dx           # Calculate profile slopes; diff() calculates elevation difference between points
slope = abs(slope)                       # Take the absolute value of the slope to avoid direction issues
slope = np.append(slope, slope[-1])      # Append one extra slope value to be same size as the area array

Above, we use np.diff to calculate the slope, but since it calculates the difference between the elevation of points, it returns one less value than in topography. To account for this, we add one extra value back to the slope variable.

P2: Passing/returning figure objects¶

When using functions with figures, it is necessary to pass the information about the figure as parameters when using any functions that update the figure. In other words, the functions will need things related to the figure in order to update them. For example, in the update_figure function you can see that ax1 and plot1 are given as values in the list of parameters used by the function. This is because the ax1 and plot1 data are updated within the function (as are time_text and elev_text). Likewise, the updated plot1 object is returned.

When you add the second subplot, you will need to be sure that any function that need the plot information has that information passed in and/or returned. This means you need to modify not only the update_figure function, but also make sure you update the list of variables passed to that function where the matplotlib animation.FuncAnimation function is called near the end of the stream_power function. Specifically, anything you pass into update_figure will need to be in the list of variables fargs in the call of animation.FuncAnimation. fargs is the list of varaibles used by the function update_figure.

P2: Units¶

Just as a reminder, the values for dhdt are m/a and the plot should have units of mm/a. We also want the erosion rate to plot as a positive value, rather than the negative values that dhdt has in the code. You can compensate for these differences when setting the y data to plot.